Lip element for instrument with flapping reed

ABSTRACT

The invention concerns a lip element for instrument with single flapping reed, for instance for clarinet or saxophone, comprising mouthpiece ( 10 ), a reed ( 12 ) and a ligature for fixing the reed ( 12 ) to the mouthpiece ( 10 ). In said mouthpiece, an insert ( 14 ) is interposed between the reed ( 12 ) and the mouthpiece ( 10 ), thereby modifying the conditions in which the two co-operate with each other, and in particular enabling to optimize the vibrational behaviour of the reed ( 12 ), by virtually modifying the table of the mouthpiece ( 10 ). The insert consists of a thin plastic or metal film provided with an adhesive and has a bevelled profile.

The present invention relates to instruments with a single beating reed,in particular to clarinets and saxophones, which include a bore formingan air column that is made to vibrate by the instrumentalist in order togenerate sounds. It concerns more specifically the portion including amouthpiece, a reed and a ligature intended to be placed in the mouth inorder to insufflate air into the instrument and make the air columnvibrate. In the present document, this portion is called the “mouthpieceassembly”, in order to avoid any confusion with the term “embouchure”which here designates exclusively the way the instrument is held in themouth. The mouthpiece includes a face or lay including a curved portionand a substantially flat portion intended to act as a support for thereed. The term “face” used without any further specificity alwaysdesignates the mouthpiece face in the following description.

In order to properly understand the operation of this type ofinstrument, reference can advantageously be made to the work entitled“Clarinette mon amie” Ernest Ferron, editions IMD 1994.

Clarinetists have been complaining, since the invention of theirinstrument, three centuries ago, about the difficulty in obtaining reedsthat perfectly satisfy their expectations. Thus, instrumentmanufacturers and inventors have sought to improve the performance ofmouthpieces and reeds. Today, it is not so much the workmanshipprecision of the reed, made of natural reed, which is questioned, butrather the intrinsic irregularities of the material of which it isformed.

A reed can be considered like a spring whose features vary as a functionof its shape, the structure of the material, its humidity level and thestate of fatigue and chemical and structural transformation of thefibers that it comprises, due to aging and light.

It often happens that the reed itself is good, but that it does notinteract in a satisfactory manner with the mouthpiece on which it isplaced. The clarinetist takes another one or reworks it in order to fitit more intimately to the mouthpiece, an activity that requiressignificant savoir-faire.

Devices intended to be associated with the mouthpiece assembly have alsobeen proposed, in order to obtain the best from available reeds, forexample particular ligature models. Such a solution is disclosed in U.S.Pat. No. 1,896,814. In the instrument disclosed, the mouthpiece includesa groove in its lay, and the ligature is arranged so as to be able toexert pressure on the groove, so as to flex the reed and thereby modifythe opening.

U.S. Pat. No. 3,791,253 discloses a ligature provided with a removablepart capable of resting on the reed. By moving this part longitudinally,it is possible to modify the elastic features of the reed.

U.S. Pat. No. 2,224,719 provides the addition of a spring exertingpressure on the inner surface of the reed, the fixing and pressure beingassured by a screw engaged in a hole comprised in the reed. Thissolution also modifies the elastic features of the reed. Moreover, thefact of piercing the reed can considerably change its behavior, in anunpredictable manner.

The improvements provided by the solutions that have just been describedare limited, since in all three cases, only one parameter is targeted.However, it seems that in addition to the elasticity of the reed, whichcan be modified by the devices disclosed in U.S. Pat. No. 3,791,253 or2,224,719, or the size of the opening comprised between the mouthpieceand the tip of the reed, which can be modified by means of the devicedisclosed in U.S. Pat. No. 1,896,814, five parameters relating to theinteraction of the mouthpiece and the reed play an essential role. Threeconcern the curved portion of the face, namely its length, its curvatureand its lateral asymmetry. Added to this are the interface conditionsbetween the reed and the mouthpiece, and the inclination of the reedwith reference to the baffle.

Other more significant modifications have been proposed, requiringrearranging the mouthpiece structure in a significant manner. Forexample, U.S. Pat. No. 2,495,484 discloses a mouthpiece assembly,provided with a frame fixed by means of screws and taking the place ofthe mouthpiece face. A fork, fixed to the mouthpiece assembly, isarranged so as to be supported against the surface of the frame oppositethe face. This type of improvement has a redhibitory drawback: that ofnot fitting the musician's instrument without any modification. Indeed,the latter has to either replace the mouthpiece that he is used to, orhave his instrument modified by a professional.

It is an object of the present invention to overcome these drawbacks, byallowing better control of all the parameters influencing theinteraction between the mouthpiece and the reed and fitting onto astandard mouthpiece—without requiring any modifications to itsstructure. According to the invention, the mouthpiece assembly includes:

-   -   a mouthpiece fitted with:        -   a chamber, including a baffle, a wall opposite the baffle or            ramp and two side walls, and a bore, for allowing air to            flow and sound waves to circulate towards the pipe of the            instrument, and        -   a first original face, including a curved portion, arranged            laterally on either side of the chamber and forming the end            of the walls, and a substantially flat portion arranged            above the chamber and the bore, in the extension of the            curved portion,    -   a reed including        -   a stock, intended to be secured to the mouthpiece,        -   a vamp intended to vibrate, and        -   a table extending over its entire length and forming one of            the surfaces of the stock and the vamp.        -   arranged to be supported, via the portion of its table            associated with the stock against the flat portion of the            first face, and    -   a ligature, for assuring the assembling of the reed on the        mouthpiece.

In this mouthpiece assembly, the mouthpiece and the reed between themdefine an opening allowing air to penetrate, to generate soundvibrations. The air then flows into the chamber and into the bore, in agenerally longitudinal direction.

-   -   The mouthpiece assembly is characterized in that it further        includes, present during the production of sound, a removable        insert taking the form of a patch, gripped between the        mouthpiece face and the reed table, and arranged so as to        define, with the first face, a second virtual face, as a        function of the forms of the first face, the insert and the        position of said insert on the first face. A patch will be        defined in the present description as being a flexible piece,        advantageously of a generally rectangular or trapezoidal shape,        whose thickness is variable and substantially smaller than the        other dimensions.

In this mouthpiece assembly, the insert can cover at least one part ofthe curved portion of the first face. Consequently, the length and/orcurvature of the curved portion can be modified, and a longitudinaldisplacement allows its features to be finely modulated.

The present invention also concerns an insert intended to be fitted tosuch a mouthpiece assembly. This insert has a chamfer at at least one ofits ends, intended to be arranged facing the vamp of the reed.Advantageously, the thickness of the end of the chamfer is less than0.09 mm.

Advantageously the thickness of the insert is constant laterally andvariable, along the longitudinal side, in accordance with a continuousfunction defined by sections, said sections, which are three in number,each being formed of a fourth degree polynomial, at least one of whichhas, over a length of more than 2 millimeters, at least two non zerocoefficients.

Advantageously the film is formed of superposed thin sheets fixed toeach other, the number of superposed sheets decreasing to form thechamfer.

In order to allow fine correction, the angle at the apex of the chamfermust be small, advantageously less than 3°.

The shape of the insert chamfer allows the features of the curvedportion of the virtual face to be modified. Several shapes can beenvisaged, selected in accordance with the modifications to be made.

In order to prevent too large a portion of the chamber being masked bythe insert, its end including the chamfer is provided with a cut outportion made in the whole of its thickness and arranged laterally in itsmedian part. This cut out portion defines two fingers arranged so as torest on the curved portion of the mouthpiece face, and a scallopingdefined by these fingers and intended to clear access to the chamberproperly.

The choice of material plays a role in the working conditions of thereed on the mouthpiece. It is also necessary for the material used toallow the desired shape to be given to the insert and for its structureto be such that it does not vibrate with the reed during the productionof sound. It is thus advantageous to use a material capable of beingworked by plastic deformation, for example an aluminum alloy.

In the event that the interface has to be made of a not very elasticmaterial, it is advantageous to make the insert in a plastic material.

If the latter is of the thermoformable type, the desired forms can beobtained by simple inexpensive means, by heating and pressing the partsto be deformed, by injection or by calendering.

It has become clear that by providing the insert with a repositionabletype of adhesive layer, on a portion of one of its faces, it is possibleto obtain sure and easily adjustable positioning. This layer can alsoact on the interface conditions between the reed and the mouthpiece. Thethickness and the surface can thus be adjusted accordingly. Generally,however, the layer does not completely cover the insert, so that thelatter can easily be detached.

Other advantages and features of the invention will appear from thefollowing description, made with reference to the annexed drawing, inwhich:

FIGS. 1 and 2 show a clarinet mouthpiece assembly according to theinvention seen respectively in perspective and from the side thereofintended to receive a reed, defined as the “top” in the presentdescription,

FIGS. 3 and 4 respectively illustrate top and side views of varioustypes of inserts capable of being fitted to the mouthpiece assemblyaccording to the invention,

FIG. 5 shows a profile view of a clarinet mouthpiece without an insert.It illustrates the system of axes Ox and Oz defined when a reed is fixedonto the substantially flat portion of the mouthpiece face, and

FIG. 6 is a graph that shows how a thin insert is calculated.

In FIGS. 1, 4 and 6, scale has not been respected. More specifically,the thickness of the inserts has been greatly exaggerated, so that theirshape is visible.

The mouthpiece assembly shown in FIGS. 1 and 2 is of the type intendedto be fitted to a clarinet. A similar model can be adapted to asaxophone or to any other instrument with a single beating reed. Itincludes a mouthpiece 10, a reed 12 and a ligature that has not beenshown in the drawing, in order to make the parts involved in theinvention more visible. As will be noted in the following description,these elements are those that are conventionally fitted to theinstrument, without having undergone any transformation, or structuraladaptation. The mouthpiece assembly also includes an insert 14, arrangedbetween mouthpiece 10 and reed 12, and whose structure and function willbe specified hereinafter.

In a conventional manner, mouthpiece 10 is made in a single part. It hasan oblong shape, with a front part 16 intended to be placed in themouth, and a cylindrical rear part, forming a tenon 18, and arranged tobe fixed to the clarinet barrel. The front part 16 has a substantiallyconical shape, truncated by two surfaces 20 and 22. Surface 20 forms aface, called here the original face, including two portions, one ofwhich 20 a, substantially flat, is close to tenon 18, and the other 20b, which is curved, occupies the front of mouthpiece 10.

Tenon 18 has a generally cylindrical shape and carries, at its peripheryand in an ad hoc concentric recess, a cork joint 24, intended to form asealed connection with the barrel.

Surface 22 forms the part of the mouthpiece called the beak and forms,with surface 20, an acute angle, which defines the whistle shape of theend of the mouthpiece, also called the tip of the mouthpiece, in thepart thereof that is placed in the mouth.

A channel passes through mouthpiece 10, connecting surface 20 to thecentral portion of tenon 18, and intended to ensure the passage of airfrom the mouth to the body of the instrument. It is formed of a chamber26—delimited by a baffle 26 a, a wall opposite the baffle or ramp andconcealed in the drawing, and two side walls 26 b—opening into portion20 b to define the part of the mouthpiece usually called the window, anda bore 27, of slightly conical form, concentric to the tenon, openinginto the chamber and extending into the barrel then into the clarinetpipe, not shown in the drawing. Bore 27 delimits a column of air, madeto vibrate via the effect of the reed vibrations and whose frequencydefines the sound emitted.

Reed 12 is formed, in a manner well known to those skilled in the art,of a plate usually made from a portion of natural reed of the Arundodonax species, having a flat lower surface which forms a table 28, astock 30, convex on the side opposite table 28, which acts as a supportfor the ligature to secure reed 12 to mouthpiece 10, and a vamp 32,whose thinned structure enables it to vibrate. In FIG. 1, the reed isshown above the mouthpiece, so as to allow insert 14 to be seen. Table28 has, however, been marked with dotted lines in its working position,identified by the reference 28′.

Insert 14 is formed of a stable and sufficiently flexible material toadhere without any difficulty to the mouthpiece face despite strongvibrations of the reed, for example aluminum or plastic material. As canbe seen in FIGS. 3 and 4, it includes a rear portion 34, forming thebody of the insert and allowing, depending upon its shape, the distanceand inclination of reed 12 to be modified with reference to mouthpiece10, a front portion 36 for adjusting the curvature features of portion20 b, and a median portion 38 connecting front and rear portions 36 and34. This median portion 38 is required to extend front portion 36 orrear portion 34, depending upon the longitudinal position of the inserton mouthpiece 10. The distinction between these three portions 34, 36and 38 is thus above all functional and not exclusively morphological,and it depends upon the curvature of the curved portion 20 b of themouthpiece face being used. The limits between portions 34, 36 and 38indicated in FIGS. 3 and 4 are thus approximate, since said curvature isnot a priori known.

In the embodiment shown in FIGS. 3 and 4, the thickness of the rearportion 34 is constant. The front portion has a chamfer 40, more clearlyvisible in FIG. 4, which thins out towards the end of mouthpiece 10, aswell as two fingers 42 and 44 each extending over one of the sides ofchamber 26 and partially covering the end of side walls 26 b anddefining a cut out portion 46 preventing chamber 26 being obstructed,even if insert 14 is arranged very far forward on mouthpiece 10. Thethickness of the chamfer at its free end has to be as small as possible,generally less than 0.09 mm, with an apex angle smaller than or equal to3°.

Until now, the reed was directly applied via its table 28, against theflat portion 20 a of the original face. Because of the curved shape ofportion 20 b, the front portions of mouthpiece 10 and reed 12 are spacedapart from each other and form an opening 48 opening into chamber 26 andallowing the clarinetist to produce a sound due to oscillations of thereed, by insufflating air. Relative to the reed, insert 14, affixed tosurface 20 and partially covering surface 20 b, forms a new face, calledhere a virtual face, having a different curvature and/or length thancurved portion 20 b, depending upon the shape of insert 14.

The quality of the sounds emitted depends upon numerous parameters,particularly on the body of the instrument, but also on reed 12 and themanner in which it vibrates on mouthpiece 10. This part of theinstrument is very sensitive to minute differences in its structure aswell as to environmental, thermal, hygrometric and barometricconditions. Each time that a clarinetist performs, he has to choose areed suited to the work to be played, the tonality of the instrumentused and the acoustic environment. In order to increase the probabilityof having an optimal reed, the clarinetist has to “wear in” a largenumber, which is expensive and tiresome. Moreover, the optimum operatingperiod of each reed is quite brief.

Insert 14 provides a simple, economic and original solution to theaforementioned problem, particularly because it fits any type ofmouthpiece, without requiring any prior modification. Such a solutionalso allows a teacher to direct his pupil to more fitting embouchure andsupport techniques, by developing his flexibility and sensitivity tovariations in sonority.

As will be specified hereinafter, the presence of this insert 14modifies the conditions linking reed 12 to mouthpiece 10, and thus, thesound quality that is a function of the form, position and materialforming insert 14.

More specifically, it has been observed that, for a given reed, thequality of the sounds generated depends, amongst other things, upon:

-   -   the dimension of the opening comprised between the mouthpiece        and the tip of the reed,    -   the length, curvature and lateral asymmetry of the curved        portion of the face,    -   the interface conditions between the reed and the mouthpiece (in        particular the elasticity, inertia and state of the surface),        and    -   the inclination of the reed with reference to the baffle.

All of these parameters can be adjusted by a suitable choice of insert,more particularly of its shape, surface state, the material of which itis formed, and its position on mouthpiece 10. The displacement of theinsert can be significant, as can be seen in FIG. 2, where insert 14 hasbeen shown in the median position, in full lines, and in the set backposition, in dotted lines, the displacement being indicated by a doublearrow.

FIGS. 3 and 4 show a range of inserts, assuring such adjustments,respectively seen from the top and the side. In these Figures,references have only been given for part of them, in order to avoidoverloading the drawing. They have, seen from above, a generallyrectangular shape. They could equally well have a trapezoidal shape, inorder to better match the shape of surface 20.

Insert 14 shown at a is rectangular, cut out from a film of constantthickness. It is intended to be inserted between the flat portion 20 aof the mouthpiece and table 28 of reed 12. The material chosen willdefine the interface qualities, whereas the thickness will assureadjustment of opening 48. This insert can also include a chamfer, asshown in FIG. 4, seen from the side, at h or j. In such case, it couldslightly overlap onto curved portion 20 b, not enough however toobstruct chamber 26 too much.

The inserts shown at b, c, d, e and f allow strong engagement on curvedportion 20 b, owing to cut out portion 46 with which they are provided,defined by fingers 42 and 44. This cut out portion 46 can have severalshapes. Thus, it is a semi-ellipse at b and trapezoidal at c. At d, thetrapezoidal shape is again shown, completed by a triangular structure.The inserts shown at e and f only include two very short fingers 42 and44, so that cut out portion 46 is small.

Insert 14, shown in perspective at g in FIG. 4, has a very simple shapewith rear portions 34 and 38 of constant thickness, whereas the frontportion 36 forms chamfer 40. It can be achieved by superposing thinsheets, from several μm to several hundredths of a millimeter inthickness, for example of thermo-adhesive plastic, the sheets beingfixed to each other by heating. It should be noted that the rear portionof the insert can be made using thicker sheets than the other parts,since the latter supports the stock of the reed whose vibration duringthe production of sound is negligible. The insert advantageously has athickness comprised between 0.01 and 1 mm.

The embodiment illustrated at h is similar to g in its structure, thechamfer 40 being, however, regular and without any steps. Such astructure can be made by means of a sheet of aluminum alloy, whose edgesare flattened in a roll mill. At i, the angle of chamfer 40 is greaterthan at h. Practice has shown that this angle is advantageously lessthan 3°, typically from 0.1 to 0.3°.

The embodiments shown at j, k and l are provided with a convex frontportion 36. Rear portion 34 is bent towards its free part at j,decreases towards median portion 38 at k, whereas at l, the insert showndoes not have a rear portion. Via the convex part of front portion 36,these latter structures allow a reduction in the length of the curvedportion of the virtual mouthpiece face. The support conditions of reed12 on portion 20 a of the mouthpiece face, and thus of opening 48, canbe modified as a function of the structure of rear portion 34.

The insert shown at m includes a thick rear portion 34 decreasingtowards median portion 38, thus considerably modifying the supportconditions of reed 12 on portion 20 a of the face of mouthpiece 10. Itsfront portion 36, forming chamfer 40, has a concave shape, which onlyslightly modifies the shape of portion 20 b in its front portion,whereas it greatly modifies its neighboring part of portion 20 a.Consequently, the length of the virtual face is increased.

It thus appears that, by adding an insert between the reed and themouthpiece of an instrument with a single beating reed, it is possibleto control the interaction between the reed and the mouthpiece in a muchmore efficient manner, and thus to draw the maximum benefit fromavailable reeds.

The shape of the inserts can also be mathematically defined, by modelingthe profile of most original mouthpiece faces found on the market. Thelatter have, in fact, a shape that corresponds with an accuracy of moreor less two hundredths of a millimeter to a continuous function f_(r),defined by sections:$\left. {f_{r}\text{:}x}\mapsto\left\{ \begin{matrix}{p_{r,a}(x)} & {{{if}\quad x} \leq k_{r}} \\{p_{r,b}(x)} & {otherwise}\end{matrix} \right. \right.$Where p_(r,a) and p_(r,h) are two fourth degree polynomials:p_(r,a): x

a_(r,0)+a_(r,1)x+a_(r,2)x²+a_(r,3)x³+a_(r,4)x⁴p_(r,b): x

b_(r,0)+b_(r,1)x+b_(r,2)x²+b_(r,3)x³+b_(r,4)x⁴the coefficientsa_(r,0),a_(r,1),a_(r,2),a_(r,3),a_(r,4),b_(r,0),b_(r,1),b_(r,2),b_(r,3),b_(r,4)and k_(r) being real constants.

Since f_(r) is continuous, we have: p_(r,a)(k_(r))=p_(r,b)(k_(r))

The longitudinal axis Ox is defined as being the line of intersectionbetween the plane of the table of a reed 12 secured to the original faceand the plane of symmetry of the mouthpiece. The origin of the system ofaxes is on the Ox axis at the tapered end of the reed. The latter iscentered laterally and arranged such that the tip of the mouthpiece alsohas 0 as the abscissa. The lateral axis Oy perpendicular to the Ox axis,is in the plane of the reed table, whereas the Oz axis is perpendicularto this latter plane (FIG. 5).

f_(r)(x) defines the ordinate at z of an abscissa point x of theoriginal mouthpiece face.

The constant k_(r) forms the limit between curved portion 20 b and thesubstantially flat portion 20 a of a face referenced by this function.If this latter portion were perfectly flat, we would thus haveb_(r,0)=b_(r,1)=b_(r,2)=b_(r,3)=b_(r,4)=0. In reality, it is generallyvery slightly concave.

In a similar manner to f_(r) we will define a function f_(v),corresponding to a virtual mouthpiece face to which an insert isaffixed: $\left. {f_{v}\text{:}x}\mapsto\left\{ \begin{matrix}{p_{v,a}(x)} & {{{if}\quad x} \leq k_{v}} \\{p_{v,b}(x)} & {otherwise}\end{matrix} \right. \right.$Where p_(v,a) and p_(v,b) are two fourth degree polynomials:p_(v,a): x

a_(v,0)+a_(v,1)x+a_(v,2)x²+a_(v,3)x³+a_(v,4)x⁴p_(v,b): x

b_(v,0)+b_(v,1)x+b_(v,2)x²+b_(v,3)x³+b_(v,4)x⁴the coefficientsa_(v,0),a_(v,1),a_(v,2),a_(v,3),a_(v,4),b_(v,0),b_(v,1),b_(v,2),b_(v,3),b_(v,4)and k_(v) being real constants.

Since f_(v) is continuous, we have: p_(r,a)(k_(r))=p_(r,b)(k_(r))

The Ox′ axis is defined as being the line of intersection between theplane of table 28 of a reed fixed to the virtual face and the plane ofsymmetry of the mouthpiece. The origin of this new system of axes isfound on the Ox′ axis, at the tapered end of the reed. This latter iscentered laterally and arranged such that the tip of the mouthpiecegenerally has 0 for abscissa. The Oy′ axis, perpendicular to the Ox′axis is in the plane of the reed table, whereas the Ox′ axis isperpendicular to this latter plane. f_(v)(x′) defines the ordinate z′ ofan abscissa point x′ of the virtual mouthpiece face.

The two defined systems of axes are thus slightly shifted with respectto each other. Since the angle of the two axes is very small, we willconsider that one abscissa point x has the same abscissa with respect tothe two axes.

It should be noted, on the other hand, that the vibrating reed can movebeyond its rest position; p_(v,a)(x) can thus have a maximum for an xabscissa, slightly less than k_(v) so as to control the reed also inthis part of its vibration, as can be seen in FIG. 6.

The inserts allow a large variety of face forms to be obtainedvirtually, from a given original face, by giving suitable values to thecoefficientsa_(v,0),a_(v,1),a_(v,2),a_(v,3),a_(v,4),b_(v,0),b_(v,1),b_(v,2),b_(v,3),b_(v,4)and k_(v).

In practice, since useful corrections are modest and the angulardifference in the reed with reference to the mouthpiece baffle inducedby the presence of the insert is small, the thickness of the insert canbe inferred directly by subtracting one function from the other thenadding an affine function d (straight line):d: x

d₀+d₁xchosen such that the function s representing its thicknesss=f_(v)−f_(r)+d is always positive over the entire length of the faceand so that it tends towards zero at the tip of the mouthpiece (more orless a tolerance of the order of a hundredth of a millimeter). Theseoperations are illustrated graphically in FIG. 6. More specifically, thefunctions f_(r),f_(v), d and s as well as the abscissas of constantsk_(r) and k_(v) are represented. It will be noted that the straight lined coincides with the Ox′ axis when the insert represented by s issuperposed on the original face of the mouthpiece represented by f_(r).It can be seen that the virtual face f_(v) with respect to a reed placedon the Ox axis is equivalent to the original face plus the insert(f_(r)+s) when a reed is placed on the Ox′ axis (taking due account ofthe fact that the scale of the Oz axis is greatly enlarged, in this caseof the order of thirty times).

Let us summarize the foregoing taking account of the mathematicalproperties of polynomials: usually, the longitudinal thickness of theinsert substantially follows a continuous function defined by sections,by means of three fourth degree polynomials, delimited by the constantsk_(r) and k_(v), as well as by the minimal thickness and the maximallength that one wishes to give it. Outside these two external limits,the thickness of the insert is zero. Generally, the thickness isconstant laterally, unless one wishes to give it lateral asymmetry.

It should be stressed that all of the embodiments illustrated in FIG. 4answer the definition of the preceding paragraph, including the insertshown at g provided that the sheets forming it are sufficiently thin.

For the record, it should be mentioned that predicting the behavior of agiven mouthpiece face of function f is difficult, from both thetechnical and musical point of view. It becomes slightly more convenientwhen a mathematical transformation is performed beforehand allowing thedistance g(x) traveled by the thinned end of a reed between its restposition and the position that it would have perfectly matching thecurvature of the face to an abscissa point x, to be calculated. The reedtable is extended then along the tangent at this point, in a perfectlyrectilinear manner to abscissa 0.

This is translated mathematically by the following differentialequation: ${f^{\prime}(x)} = \frac{{f(x)} - {g(x)}}{x}$Where f′ is the first derivative of function f. Assuming that function gis a fourth degree polynomial,g: x

c₀+c₁x+c₂x²+c₃x³+c₄x⁴the differential equation can be resolved: one obtains:${f(x)} = {c_{0} - {c_{1}x\quad{\ln(x)}} - {c_{2}x^{2}} - {\frac{1}{2}c_{3}x^{3}} - {\frac{1}{3}c_{4}x^{4}} - {hx}}$where the integration constant h has a value:$h = \frac{c_{0} - {c_{1}x_{0}\quad{\ln\left( x_{0} \right)}} - {c_{2}x_{0}^{2}} - {\frac{1}{2}c_{3}x_{0}^{3}} - {\frac{1}{3}c_{4}x_{0}^{4}}}{x_{0}}$x₀ being a real zero of the function g such thatg(x ₀)=f(x ₀)=0.

The volume of air v displaced by the reed between the position g(0) andthe position g(x) of its thinned end can be calculated by the function:$\left. {{\mathcal{v}}\text{:}\quad x}\mapsto{{\frac{1}{4}c_{1}x^{2}} + {\frac{1}{3}c_{2}x^{3}} + {\frac{3}{8}c_{3}x^{4}} + {\frac{2}{5}c_{4}x^{5}}} \right.$

Empirical tests have demonstrated that it is possible to neglect thecoefficient c₁, which then means that f is a fourth degree polynomialand that g′(0)=0.

Using the equations hereinbefore and the shape of the reed, a materialengineer can estimate the stress that the reed undergoes during soundproduction. It is thus possible to create a range of inserts controllingthe intensity and positioning of the stresses that one wishes the reedto undergo so as to optimize its longevity.

Empirically, it has been observed that the latter can be seriouslyprolonged, starting by exploiting the elastic potential of a new reedwhere it is very thick, using a mouthpiece face combining the followingfeatures: small opening, large length and small curvature. Progressivelyas the reed becomes suppler, it is possible to stress increasingly thezones where the reed is thinner by increasing the opening and thecurvature while reducing the length. Using a conventional mouthpiecewithout using the insert, the instrumentalist would be obliged tocompress the reed with his lips and consequently exploit a thinner zoneof the reed. Once this zone is weakened, it is no longer possible to usethicker zones with a musically satisfactory result, which considerablydecreases the longevity of the reed.

In order to use the insert and in order to facilitate the positioningthereof, while allowing it to move, its surface intended to come intocontact with the face of mouthpiece 10 is advantageously coated with alayer of adhesive of the repositionable type such as those marketed by3M® (USA). This layer of relatively soft material modifies the interfaceconditions between reed 12 and mouthpiece 10, which is why it may beadvantageous for it to be applied only over a small portion of thelength of the insert, chosen according to the desired result. In allcases, it is preferable for it not to totally cover the surface of theinsert, in order to facilitate its removal.

It is evident that the embodiments given here represent only an exampleof the possible solutions. Other materials could thus be implemented,chosen for their rigidity, their elasticity or their ability to dampen avibration, as well as for their ease of use.

It is also possible to provide other insert shapes, both as regardsfront portion 36, rear portion 34 and median portion 38. it is thuspossible to have a thickness that varies laterally, such that the insertis thicker on the edges, or conversely, thinner, or exhibiting lateralasymmetry, such that the curvatures of the virtual face are not the sameon either side of chamber 26. Such an arrangement allows the effect ofany asymmetry in the clarinetist's mouth to be corrected, as well asthat of the reed, and more gradual control of the acoustic power.

In order to improve the fixing of the inserts to mouthpiece 10, it isalso possible to make inserts provided with lateral positioning means,made by folding its front portion 36, engaging in chamber 26 and/ormatching the shape of the exterior of mouthpiece 10.

The solution described with reference to a mouthpiece assembly for aclarinet is, of course, also applicable to other instruments with asingle beating reed, particularly to the saxophone. The dimensions ofthe inserts will then be adapted to this instrument.

It is also possible to place several superposed or juxtaposed inserts toobtain the desired effect.

Generally, insert 14 is affixed to the face of mouthpiece 10. One could,however, also envisage applying it to table 28 of reed 12.

In order to facilitate the adjustment of the insert's position, it isadvantageous to provide it with an index or a scale referencing itslongitudinal position that the instrumentalist will have to match to amark on the mouthpiece, like for example, the first centering ring ofthe ligature.

1. Mouthpiece assembly for a reed instrument, including: a mouthpiece(10) provided with: a chamber (26), including a baffle (26 a), a wallopposite the baffle or ramp and two side walls (26 b), and a bore (27),for allowing air to flow and sound waves to circulate towards the pipeof the instrument, and a first original face, including a curved portion(20 b), arranged laterally on either side of the chamber (26) andforming the end of said walls (26 b), and a substantially flat portion(20 a) arranged above the chamber (26) and the bore (27), in theextension of the curved portion (20 b), a reed (12) including a stock(30), intended to be secured to the mouthpiece, a vamp (32) intended tovibrate, and a table (28), extending over its entire length and formingone of the surfaces of the stock (30) and the vamp (32), arranged to besupported, via the portion of its table (28) associated with the stock(30) against the flat portion (20 a) of the first face, and a ligature,for assuring the assembling of the reed (12) on the mouthpiece (10),wherein the mouthpiece (10) and the reed (12) define between them anoperating (48) allowing air to penetrate, to generate sound vibrations,the air then flowing into the chamber (26) and into the bore (27), in agenerally longitudinal direction, characterized in that it furtherincludes, present during the production of sound, a removable insert(14) taking the form of a patch, gripped between the mouthpiece face(20) and the reed table (28), and arranged so as to define, with thefirst face, a second virtual face, as a function of the forms of thefirst face (20), the insert (14) and the position of said insert (14) onthe first face (20).
 2. Mouthpiece assembly according to claim 1,characterized in that said insert (14) covers a part of said curvedportion (20 b).
 3. Insert (14) intended to be gripped between the reed(12) and the mouthpiece (10) of the mouthpiece assembly according toclaim 1, characterized in that it has a chamfer (40) at at least one ofits ends intended to be arranged facing the vamp (32) of the reed (12).4. Insert according to claim 3, characterized in that its thickness isvariable along the longitudinal side, substantially following acontinuous function defined by sections, said sections being three innumber and each being formed of a fourth degree polynomial, one ofwhich, over a length of more than 2 millimeters, has at least two nonzero coefficients.
 5. Insert according to claim 3, characterized in thatthe thickness of the end of said chamfer is less than 0.09 millimeters.6. Insert according to claim 3, characterized in that said film isformed of superposed thin sheets fixed to each other, the number ofsuperposed sheets decreasing to form said chamfer (40).
 7. Insertaccording to claim 3, characterized in that the angle at the apex ofsaid chamfer (40) is less than 3°.
 8. Insert according to claim 3,characterized in that its end (36) including said chamfer (40) isprovided with a cut out portion (46) made in its entire thickness andarranged laterally in its median portion.
 9. Insert according to claim8, characterized in that said cut out portion (46), intended to improvethe clearing of access to the chamber (26), is defined by two fingers(42, 44) arranged so as to rest on said curved portion (20 b). 10.Insert according to claim 3, characterized in that it is formed of amaterial capable of being worked by plastic transformation.
 11. Insertaccording to claim 10, characterized in that said material is analuminum alloy.
 12. Insert according to claim 10, characterized in thatsaid material is a plastic material.
 13. Insert according to claim 12,characterized in that said material is of the thermoformable type. 14.Insert according to claim 3, characterized in that at least one part ofits surface intended to be in contact with the reed (12) and/or themouthpiece (10) is provided with a repositionable type adhesive layer.15. Insert according to claim 4, characterized in that the thickness ofthe end of said chamfer is less than 0.09 millimeters.
 16. Insertaccording to claim 4, characterized in that said film is formed ofsuperposed thin sheets fixed to each other, the number of superposedsheets decreasing to form said chamfer (40).
 17. Insert according toclaim 5, characterized in that said film is formed of superposed thinsheets fixed to each other, the number of superposed sheets decreasingto form said chamfer (40).
 18. Insert according to claim 4,characterized in that the angle at the apex of said chamfer (40) is lessthan 3°.
 19. Insert according to claim 5, characterized in that theangle at the apex of said chamfer (40) is less than 3°.
 20. Insertaccording to claim 6, characterized in that the angle at the apex ofsaid chamfer (40) is less than 3°.